A football is kicked into the air. Its height in meters after t seconds is given by h(t)=-4.9 (t-2.4)^2+29.
A. What was the height of the football when it was kicked?
B. What is the maximum height of the kick?
C. How long did it take for the football to reach its maximum?
D. How high was the ball after 2 seconds?
A. To find the height of the football when it was kicked, we need to substitute t=0 into the height equation.
h(0) = -4.9 (0 - 2.4)^2 + 29 = -4.9 (-2.4)^2 + 29 = -4.9 (5.76) + 29 = -28.224 + 29 = 0.776
Therefore, the height of the football when it was kicked was approximately 0.776 meters.
B. To find the maximum height of the kick, we need to find the vertex of the quadratic equation. The vertex can be found using the formula t = -b / (2a), where a = -4.9 and b = -4.9 × 2.4 × 2.
t = -(-4.9 × 2.4 × 2) / (2 × -4.9) = 2.4
To find the corresponding height, substitute the value of t back into the height equation:
h(2.4) = -4.9 (2.4 - 2.4)^2 + 29 = -4.9 (0)^2 + 29 = 29
Therefore, the maximum height of the kick is 29 meters.
C. The time it takes for the football to reach its maximum height can be determined from the x-coordinate of the vertex, which is 2.4 seconds.
Therefore, it takes 2.4 seconds for the football to reach its maximum height.
D. To find the height of the ball after 2 seconds, substitute t=2 into the height equation:
h(2) = -4.9 (2 - 2.4)^2 + 29 = -4.9 (-0.4)^2 + 29 = -4.9 (0.16) + 29 = -0.784 + 29 = 28.216
Therefore, the ball was approximately 28.216 meters high after 2 seconds.
To answer these questions, we need to understand the equation that represents the height of the football. The equation given is h(t) = -4.9(t-2.4)^2 + 29. This equation is in the form of a quadratic function, where h(t) represents the height in meters at time t.
A. What was the height of the football when it was kicked?
To find the height of the football when it was kicked, we can substitute t = 0 into the equation:
h(0) = -4.9(0-2.4)^2 + 29
Now, calculate the value of h(0).
B. What is the maximum height of the kick?
The maximum height of the kick represents the vertex point of the quadratic equation. We can use the equation -b/2a to find the t-value at the vertex, where a, b, and c are coefficients of the quadratic equation in the form ax^2 + bx + c. In this case, t is the variable representing time, and the quadratic equation is -4.9(t-2.4)^2 + 29. Once we find the t-value at the vertex, we can substitute it back into the equation to determine the maximum height.
C. How long did it take for the football to reach its maximum?
As mentioned in the previous answer, we need to find the t-value at the vertex to determine the time it took for the football to reach its maximum height.
D. How high was the ball after 2 seconds?
To find the height of the ball after 2 seconds, we can substitute t = 2 into the equation:
h(2) = -4.9(2-2.4)^2 + 29
Now, calculate the value of h(2).
A plug in t=0
B as with any parabola, the vertex is at t = -b/2a
C see B
D plug in t=2